Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def binarySearch (arr, l, r, x): 
  if r >= l: 
    mid = int(l + (r - l)/2)
    if arr[mid] == x: 
      return mid 
    elif arr[mid] > x: 
      return binarySearch(arr, l, mid-1, x) 
    else: 
      return binarySearch(arr, mid + 1, r, x) 
  else: 
    return -1
def b():
  number = int(input())
  a = [0]
  if number != 1:
    for i in range(1, (10**5)+1):
      a.append(a[i-1] + i)
    for i in range(1, (10**5)+1):
      if binarySearch(a, 1, len(a)-1, number-a[i]) != -1:
        print("Yes")
        return
    
  print("No")
b()